EP3152903B1 - Précision adaptative et quantification d'une matrice transformée par ondelettes - Google Patents

Précision adaptative et quantification d'une matrice transformée par ondelettes Download PDF

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EP3152903B1
EP3152903B1 EP15767201.5A EP15767201A EP3152903B1 EP 3152903 B1 EP3152903 B1 EP 3152903B1 EP 15767201 A EP15767201 A EP 15767201A EP 3152903 B1 EP3152903 B1 EP 3152903B1
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matrix
level
fixed
wavelet
matrices
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EP3152903A1 (fr
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Than Marc-Eric Gervais
Bruno Loubet
Nicolas BESSOU
Yves GUIMIOT
Mickael PETITFILS
Sebastien ROQUES
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
    • H04N19/63—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets
    • H04N19/635—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets characterised by filter definition or implementation details
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/124—Quantisation
    • H04N19/126—Details of normalisation or weighting functions, e.g. normalisation matrices or variable uniform quantisers
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
    • H04N19/18—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being a set of transform coefficients
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/42—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals characterised by implementation details or hardware specially adapted for video compression or decompression, e.g. dedicated software implementation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/50—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using predictive coding

Definitions

  • the present invention relates to the field of matrix coding; it is notably applicable to the encoding of media, particularly image or video media, in the form of digital files. It relates more particularly to a process for reducing the entropy of these files, as defined by Shannon's formula, defined below.
  • Shannon's entropy defines the "amount" of information present in a signal, and therefore gives an accurate indication of the amount of bits needed to encode that signal using binary encoding techniques such as arithmetic encoding or Huffman coding. The more repetitive and evenly distributed the values are in the signal, the lower the entropy of this signal.
  • Wavelet transforms are used to reduce the size of digital files. This is particularly the case with certain digital image compression formats, such as jpeg2000.
  • the wavelet transformation of a matrix consists in dividing this matrix into a so-called approximation matrix or matrix L, and a so-called details matrix or matrix H.
  • Each of these matrices contains approximately half the values of the original matrix .
  • the approximation matrix L corresponds to a "reduced image" of the original matrix
  • the detail matrix H corresponds to the details removed to reduce the size of the matrix.
  • the wavelet transformation In the context of two-dimensional wavelet transformations, it is possible to use the wavelet transformation horizontally or vertically. Usually, the transformation is performed in one direction (for example, vertically) to obtain an approximation matrix of type L and a matrix of details of type H, then in the reverse direction (for example, horizontally) on each of the matrices of type L and H.
  • the application of this second transform on the approximation matrix of type L generates an approximation matrix of type LL and a matrix of details of type LH.
  • Applying this second transform to the H-type detail matrix generates two HL-type and HH-type detail matrices.
  • the successive application of transformations in both directions will be called the wavelet level below to obtain an approximation matrix LL and three detail matrices HL, LH and HH as explained above.
  • the LH, HL and HH type detail matrices are usually quantized to reduce their entropy, while a new level d 'wavelets can be applied to the LL-type matrix. It is thus possible to apply as many levels as necessary on the successive LL-type approximation matrices.
  • the jpeg2000 additionally uses scalar dead zone quantization.
  • Some wavelet transforms are lossless; however, the application of a quantization to each wavelet level leads to rounding errors which accumulate as one advances in the successive levels, first during the compression, then during the restitution compressed digital files. This rounding problem only arises when the LH, HL, HH type detail matrices associated with the level are quantified.
  • the aim of the invention is therefore to provide a method for reducing rounding errors during the compression of a digital file when using a wavelet transform.
  • a method according to the invention, for reducing the entropy of an original matrix is mentioned in claim 1.
  • the quantization coefficient of each of the detail sub-matrices of a wavelet level is less than or equal to that of the equivalent detail matrix of the previous level. It is also, preferably, a uniform scalar quantifier, that is to say unique for each matrix of details, whatever the divided value.
  • the values of the detail sub-matrices can be quantized according to each of their quantization coefficients and then transformed into whole numbers, that is to say by dropping the digits used for the fixed point calculation.
  • the values of said approximation matrix can be transformed into integers if each of the quantization coefficients of each of the detail matrices of the next wavelet level is equal to 1, and be kept in fixed-point numbers otherwise.
  • the last LL-type approximation matrix is transformed into an integer if the last level is treated as a fixed point.
  • At least one of the quantization coefficients of each of the detail matrices of the first level is greater than 1, all the values of the original matrix are advantageously transformed into numbers with fixed points before the calculation of the first level of transformation into wavelets.
  • the numbers with fixed points are preferably obtained by reducing the number of digits to obtain said first number.
  • the method advantageously comprises an inverse wavelet transformation of the transformed matrix, the calculation of said inverse wavelet transform being carried out as a fixed point number using at least a second number of digits. equal to 1 after the decimal point, at least for each level of wavelets for which at least one of the quantization coefficients of the detail matrices of this level is strictly greater than 1.
  • the values of the detail matrices can be converted to fixed-point numbers and de-quantized before transforming to inverse wavelets.
  • the approximation matrix for that level is integer, it will be converted to fixed points before performing the inverse wavelet level, which will give the restored approximation matrix that will be used at the next level.
  • the restored matrix is advantageously obtained by performing the inverse wavelet transformations, the de-quantifications and the conversions between integers and fixed commas on all the available levels.
  • the intermediate restored matrix can advantageously be obtained by performing the inverse wavelet transformations, the de-quantifications and the conversions between integers and fixed commas on a number of levels smaller than the total number of levels available. If the wavelet level corresponding to the last inverse wavelet transformation performed is treated as fixed-point numbers, the numbers in the matrix
  • the intermediate restored value obtained are preferably fixed-point numbers with a precision comprising a number of digits equal to the second number of digits after the decimal point. For further processing of the intermediate restored matrix, each of the values of this restored matrix can be transformed into an integer.
  • the intermediate restored matrix can be used with a number of levels corresponding to the levels for which all of the data is available. Likewise, for an application requiring a resolution lower than that of the restored matrix, it is possible to use the intermediate restored matrix with the smallest number of level making it possible to achieve at least said lower resolution.
  • the numbers of the resulting restored matrix can be fixed-point numbers with precision including a number of digits equal to the second number of digits after the decimal point.
  • each of the values of said restored matrix can be transformed into an integer.
  • the inverse wavelet transform can be followed by an inverse colorimetric transform in fixed point numbers with a number of digits greater than that used for the inverse wavelet transform.
  • each value of the matrix can be shifted to the left by D digit.
  • the calculation of the inverse wavelet transform is preferably done in fixed point, using a second number of digits at least equal to 1 after the point, at least for each level of wavelets having at least one detail matrix having a quantization coefficient greater than 1.
  • the first and the second number of digits may be identical.
  • the original matrix can represent, at least partially, an image, for example represent one of the components Y, Cb and Cr of the image.
  • the first D digits resulting from the YCbCr transform are kept.
  • the YCbCr transform can be carried out with a precision greater than D digits. In this case, the precision of the data is reduced to be reduced to D digits.
  • the wavelet transform can be a 5/3 Cohen-Daubechies-Feauveau (CDF) transform with a lifting scheme.
  • CDF 5/3 Cohen-Daubechies-Feauveau
  • FIG. 1 illustrates an original black and white image constituting an image matrix of 8 rows and 8 columns.
  • the figure 2A illustrates the matrix X representing the luminance values of the pixels of the original image, each cell of the matrix arranged at the intersection of a horizontal line i (if after, line) and a vertical line j (ci -after, column) includes a literal value xij representing the luminance of a pixel located, in the original image, on the same row i and the same column j.
  • the figure 2B illustrates the same matrix X, in which each literal value has been replaced by the corresponding numeric value for the original image 1.
  • These values are encoded in unsigned integers on 8 bits, that is to say between 0 and 255
  • Applying the entropy formula gives an entropy of 5.625 for this matrix.
  • the wavelet transform used in the examples which follow is a 5/3 Cohen-Daubechies-Feauveau (CDF) transform with a lifting scheme. This differs from the wavelets used in the Jpeg2000 i.e. CDF 5/3 without loss (lossless) and CDF 9/7 with losses (lossy), only by the number of adjacent values used for details and factors associates.
  • CDF 5/3 Cohen-Daubechies-Feauveau
  • the CDF 5/3 wavelets can be applied to a Y matrix whose values are indexed as defined above.
  • the figures 3B and 4B illustrate the application of the first wavelet level NI to the original matrix X, according to the method of the prior art, before application of the quantization factors.
  • each of four lines of eight pixels, shown in figures 3A and 3B are obtained by applying vertical wavelets to the original matrix X.
  • the figure 5B illustrates the result of the application of a first step of a second level N2 of wavelets to the sub-matrix LL1Z, obtained previously; this results in the two sub-matrices L2Z and H2Z.
  • the figure 6B illustrates the result of applying a second step of this second wavelet level to the L2Z and H2Z matrices, resulting in the LL2Z, LH2Z, HL2Z and HH2Z sub-matrices of the figure 6B .
  • the LL2Z sub-matrix will therefore be kept as it is, will not be subject to a new wavelet level and will be stored in the form of an LL2QZ matrix having identical values.
  • the respective quantifications are then applied for each level.
  • the quantized sub-matrices LH1QZ, HL1QZ and HH1QZ by dividing respectively each of the values of the sub-matrices LH1Z, HL1Z and HH1Z by their quantification factors Q LH1 , Q HL1 and Q HH1 , equal to the factor Q1 of the first level NI and rounding it off according to the rule defined above.
  • the TZ transform of the matrix X by the method of the prior art is obtained by transforming the values of the original matrix X into values of the sub-matrices LL2QZ, LH2QZ, HL2QZ, HH2QZ, LH1QZ, HL1QZ and HH1QZ. These new values can be stored in specific locations. They can also replace the values of the matrix X to form a matrix of the same size.
  • the figure 8B illustrates an example of such a placement of values.
  • a method according to the invention consists in keeping, during the calculation of the wavelet transform, D digits after the decimal point (in binary notation) or D twoimals. To make the calculation faster, rather than doing it in a floating point, it is done in a fixed point. To do this, we can multiply each value of the original matrix X by a shift coefficient equal to 2 D , i.e. by (10 D ) 2 . It is also possible to shift the values, noted in binary, by D digits to the left. Only the integer part of the increased values thus obtained is then kept, so that the numbers handled are integers of which the last D digits represent the D twoimals and the other digits represent the integer part of the original number.
  • the XD matrix of increased values is shown in figure 2C .
  • the respective quantifications are then applied for each level and the values obtained are divided by 8.
  • the binary values obtained after division by the respective quantization factor can alternatively be shifted by three digits to the right.
  • the quantified sub-matrices LH2Q, HL2Q and HH2Q illustrated in figure 7C by dividing respectively each of the values of the sub-matrices LH2, HL2 and HH2 by 8 times their quantization factors Q LH2 , Q HL2 and Q HH2 , that is for each matrix 8xQ2 and taking the rounding according to the rule defined above.
  • the LL2Q sub-matrix illustrated in figure 7C is obtained by re-transforming the LL2 matrix into an integer, therefore by dividing the values of the LL2 matrix by 8 and taking the rounding according to the rule defined above. All of these transformed matrices are illustrated in figure 7C .
  • the transform T of the matrix by the method according to the invention is obtained by transforming the values of the original matrix X into values of the sub-matrices LL2Q, LH2Q, HL2Q, HH2Q, LH1Q, HL1Q and HH1Q. These new values can be stored in specific locations. They can also replace the values of the matrix X to form a matrix of the same size.
  • the figure 8C illustrates an example of such a placement of values.
  • Each of the LL0Rij values of the LL0R matrix is then divided by 8, or else the corresponding binary values are shifted by 3 digits to the right, and each of the values XRij thus obtained is rounded off according to the rule defined above.
  • Each value XRij represents the luminance of a pixel of an image restored, by a method according to the invention, of the original image.
  • Each value Eij of the matrix E represents the differences between the values XRij of the restored matrix XR and the values Xij of the original matrix.
  • the average of these deviations in the example shown, is approximately 0.78.
  • This possibility of progressive decompression allows to have a preview of the image when all the data is not available. This can be advantageously used when downloading a large image file, to decompress the image to the last fully available level before the image completes.
  • the level 2 inverse wavelets are then applied to the LL2RZ, LH2RZ, HL2RZ and HH2RZ sub-matrices in order to obtain, at the end of a horizontal inverse wavelet transform, the L2RZ and H2RZ sub-matrices illustrated in figure 10B , then, after a wavelet transform vertical inverse of the L2RZ and H2RZ sub-matrices, the LL1RZ sub-matrix, illustrated on figure 11B .
  • the level 1 inverse wavelets are then applied to the LL1RZ, LH1RZ, HL1RZ and HH1RZ sub-matrices in order to obtain, at the end of a horizontal inverse wavelet transform, the L1RZ and H1RZ sub-matrices illustrated in figure 12B , then, at the end of a vertical inverse wavelet transform of the L1RZ and H1RZ sub-matrices, the restored XRZ matrix, illustrated on figure 13B , the XRZij values of this matrix being rounded according to the rule defined above.
  • Each value XRZij represents the luminance of a pixel of an image restored, according to the method of the prior art, of the original image.
  • Each EZij value of the EZ matrix shown in figure 14B , represents the differences between the values XRZij of the restored matrix XRZ and the values Xij of the original matrix X.
  • the average of these differences in the example illustrated, is approximately 1.56.
  • the differences obtained by the method of the prior art are approximately twice as high as those obtained by a method according to the invention (0.78).
  • a method according to the invention therefore makes it possible to reduce the entropy of a matrix while obtaining a more exact restitution of the values of the matrix than by entropy reduction methods used in the prior art.
  • the black image is white can be the illustration of an R, G or B component of an RGB image.
  • Each Y, Cb or Cr component of an RGB image that has undergone a YCbCr transform, and mainly the Y luminance component can also be processed in the same way as the black and white image of the example described above. It can more generally represent any component of an image, which can also be derived from a CMYK space, or from any colorimetric transformation obtained from the RGB components, with or without loss.
  • the wavelets were first applied vertically for each level, it is also possible to apply them, for each level, first horizontally, then vertically.
  • the number of additional digits, that is to say the number oftecimals, used in the fixed-point calculation is different when calculating the Tij values of the transform T, from that used to restore the values XRij from the transform.
  • the number of digits will be greater if the number of wavelet levels is greater.
  • each of the values of the detail matrices was simultaneously quantized and divided by the offset coefficient; on the contrary, the quantization may not be done simultaneously with the division by the shift coefficient. Further, quantization and / or division by the offset coefficient can be done each time a corresponding submatrix is obtained.
  • the calculation precision was greater than the precision of the input data, which were whole numbers.
  • the input data has a precision greater than the calculation precision, in particular if it comes from a colorimetric transformation having a calculation precision greater than that of the wavelets, the XD matrix is obtained by reducing the number by twoimals and not by increasing it.
  • the precision of the data can be directly increased to be the same as that of the inverse wavelet transform. of further processing.
  • the invention can also be applied to dies with one or more dimensions.
  • a wavelet level is obtained by a series of transformations according to each of the dimensions.

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EP15767201.5A 2014-06-04 2015-07-09 Précision adaptative et quantification d'une matrice transformée par ondelettes Active EP3152903B1 (fr)

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FR1401280A FR3022064A1 (fr) 2014-06-04 2014-06-04 Precision adaptative et quantification d'une matrice transformee par ondelettes
PCT/FR2015/000141 WO2015185810A1 (fr) 2014-06-04 2015-07-09 Précision adaptative et quantification d'une matrice transformée par ondelettes

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JP6684229B2 (ja) 2020-04-22
EP3152903A1 (fr) 2017-04-12
KR20180018253A (ko) 2018-02-21
JP2017525185A (ja) 2017-08-31
FR3022064A1 (fr) 2015-12-11
CN106664408A (zh) 2017-05-10
WO2015185810A1 (fr) 2015-12-10
WO2015185810A4 (fr) 2016-03-03
BR112016028199A2 (pt) 2018-07-03
WO2015185810A8 (fr) 2016-01-14
CN106664408B (zh) 2019-08-20
US20170195673A1 (en) 2017-07-06
CA2989785A1 (en) 2015-12-10

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